Lucky Star and NGE in the same sentence? My world asplode.
Anyway, there's The Melancholy of Haruhi Suzumiya (even if the first two or so real episodes are filler, oddly enough), and Azumanga Daioh, which are more moe than, say, Elfen Leid and NGE, but both good in their own ways (Haruhi being a post-modern, clever, and ultimately captivating series, and Azumanga Daioh being Lucky Star minus the otaku stuff and plus slightly deeper characters).
There's also Cowboy BeBop, which is kind of a classic, Trigun, which I'm about halfway through right now and is shaping up to be very good indeed, and Fullmetal Alchemist, which I watched about a fifth of and plan to come back to eventually. Planetes starts off kind of weak but gets significantly better as it goes along, so I'd still recommend it.
If you liked NGE, as you said, then I also recommend the Rebuild of Evangelion movies. The first one is more or less a straight re-telling of the first six episodes, but the second one goes in a very different direction. I can't properly describe it without making this a tl;dr post, but even though it's very different in a lot of ways, it's still great for much the same reasons as the original was great.
